Switch your thermostat to the “On” position, if it isn’t already set.
Pull the faceplate off of your thermostat with your fingers. The faceplate should just pop off. This will expose the internal wiring of the thermostat.
Locate the small strip of bimetal inside your thermostat. Some bimetals are coiled.
Plug in a hairdryer, and turn it to the hottest settings. Aim the hairdryer at your bimetal. Within a few seconds, the air conditioner should turn on as the bimetal responds to the heat inside the thermostat.
Replace your thermostat, if the air conditioner does not respond to the bimetal heating.